Basic Formal Ontology 2.0
DRAFT DOCUMENT
Corresponding author: Barry Smith
2/8/2016 8:28 PM
Summary of most important changes (as compared to BFO 1.1)
•
Clarification of BFO:object
The document emphasizes that Object, Fiat Object Part and Object Aggregate are not intended to
be exhaustive of Material Entity. Users are invited to propose new subcategories of Material Entity
The document provides a more extensive account of what 'Object' means (roughly: an object is a
maximal causally unified material entity); it offers three paradigms of causal unity (for cells and
organisms, for solid portions of matter, and for engineered artifacts)
•
New simplified treatment of boundaries and regions
In BFO 1.1 the assumption was made the external surface of a material entity such as a cell could
be treated as if it were a boundary in the mathematical sense. The new document embraces the
view that when we talk about a 'surface' there, then we are talking about something fiat.
The focus in discussion of boundaries is now on fiat boundaries, which means: boundaries for
which there is no assumption that they coincide with physical discontinuities. Boundaries thus
become more closely allied with spatial regions.
•
Treatment of process predications under the heading ‘Process profiles’
To assert, for example, that this process is a 72 beats per minute process, is not to ascribe a quality
to the process, but rather to assert that there is a certain structural part of the process, called a
'beat profile', which instantiates the determinate universal: 72 beats per minute process.

Still missing
Treatment of frame-dependence of regions of space and of regions of time
Exhaustive treatment of instance-level relations; definitions of type-level relations.
Acknowledgments/Authors: Mauricio Almeida, Mathias Brochhausen, Werner Ceusters, Albert
Goldfain, Pierre Grenon, Janna Hastings, Chris Mungall, Darren Natale, Fabian Neuhaus, Alan
Ruttenberg, Mark Ressler + NAMES TO BE ADDED
The references supplied are for preliminary orientation only. Axioms and definitions included
therein are not necessarily in conformity with the content of this document.
Use of bold face indicates a label for an instance-level relation. Use of italic indicates a BFO term.
Contents
Introduction ........................................................................................................................................ 1
1. Entity ............................................................................................................................................... 2
Relations of parthood ..................................................................................................................... 3
2. Continuant ....................................................................................................................................... 4
Relation of specific dependence ..................................................................................................... 5
2.1 Independent Continuant............................................................................................................ 6
2.1.1 Material entity ...................................................................................................................... 7
2.1.1.1 Object .......................................................................................................................... 8
2.1.1.2 Object aggregate ....................................................................................................... 13
2.1.1.3 Fiat object part .......................................................................................................... 14
2.1.2 Immaterial entity ................................................................................................................ 16
2.1.2.1 Continuant fiat boundary .......................................................................................... 16
2.1.2.1.1 Zero-dimensional continuant fiat boundary ...................................................... 17
2.1.2.1.2 One-dimensional continuant fiat boundary ....................................................... 18
2.1.2.1.3 Two-dimensional continuant fiat boundary ...................................................... 18
2.1.2.3 Spatial region............................................................................................................. 20
2.1.2.3.1 Zero-dimensional spatial region......................................................................... 21
2.1.2.3.2 One-dimensional spatial region (aka spatial line) .............................................. 21
2.1.2.3.3 Two-dimensional spatial region (aka spatial volume)........................................ 22
2.1.2.3.4 Three-dimensional spatial region...................................................................... 22
Location relations .......................................................................................................................... 22
Relation of containment ............................................................................................................... 23
2.2 Specifically dependent continuant .......................................................................................... 23
Relation of specific dependence ................................................................................................... 23
2.2.1 Quality ................................................................................................................................. 24
2.2.1.1 Relational quality....................................................................................................... 25
2.2.2 Realizable entity .................................................................................................................. 25
Relation of realization ................................................................................................................... 25
2.2.2.1Role (Externally-Grounded Realizable entity) ............................................................ 26
2.2.2.2Disposition (Internally-Grounded Realizable entity).................................................. 27
2.2.2.3Function ..................................................................................................................... 28
2.3 Generically dependent continuant ......................................................................................... 29
Relation of concretization ............................................................................................................. 31
3. Occurrent ....................................................................................................................................... 32
Occupies relation .......................................................................................................................... 33
Relation of temporal parthood ..................................................................................................... 34
Relation of boundary-dependence for occurrents ........................................................................ 34
Process .............................................................................................................................................. 35
Process boundary .............................................................................................................................. 35
Spatiotemporal region ...................................................................................................................... 45
Temporal region ................................................................................................................................ 46
Zero-dimensional temporal region ....................................................................................... 46
One-dimensional temporal region ........................................................................................ 46
1
Introduction
This document is a guide for those using Basic Formal Ontology (BFO) as an upper-level ontology to
support the creation of domain ontologies containing terms referring to particulars of different sorts.
BFO is a formal ontology, which means that it is designed to be neutral with regard to the material
domains to which it is applied. The application of a formal ontology such as BFO brings benefits of
reuse, cumulation of data, and reasoning, and provides a set of common formal theories (for example
of mereotopology [5] and of qualitative spatial reasoning [18]) which do not need to be redeveloped
for each successive domain. For such benefits to be achievable, however, BFO must be capable of
being applied to material domains and in what follows we document how such application is to be
effected. We describe the conditions which must be satisfied by entities of given sorts if they are
properly to be categorized as instantiating the different universals recognized by BFO and we
provide a summary of the associated relations.
To specify these conditions we will utilize a semi-formalized English that has approximately the
expressivity of first-order logic (FOL) with identity. In a future document we will provide a
formalized treatment of these specifications using FOL; a parallel effort is also underway using
OWL.
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1. Entity
We distinguish primitive and defined terms and relation expressions. The former are so basic to our
understanding of reality that there is no way of defining them in a non-circular fashion. For these
terms, therefore, we can provide only elucidations, supplemented by examples and by axioms.
Elucidation: An entity is anything that exists.
Axiom: Entities may be either particular or also universal. [22, 19]
In this document we concentrate primarily on entities which are particulars and on the relations
between particulars elsewhere called ‘instance-level relations’ [16]. That is, the categories discussed
below are in every case categories of particulars (their extensions are groups or collections of
particulars in reality). Because BFO is the ontology that forms the basis of the Information Artifact
Ontology and universals are included among the targets of the IAO: about relation, BFO must
include universals within its domain of discourse.
We use ‘universal’ and ‘type’ as synonyms, and employ ‘category’ to refer to the higher-level
universals to which BFO terms refer. These and related technical terms of ontology are elucidated
further in [19, 25, 17].
Attributive classes
Often, language is used to refer to subgroups of entities which instantiate a given universal but do not
correspond to any subuniversal. We refer to such subgroups as ‘attribute classes’ (labeled ‘defined
classes’ in [25]). Examples are: animal owned by the emperor, tuberculosis diagnosed on a
Wednesday, surgical procedure performed in Albania. In some cases, terms of this sort need to be
included in domain ontologies. The terms in question should then be defined as children of the
corresponding genus (here: animal and tuberculosis, respectively), but they should not treated be as
part of the asserted hierarchy of the ontology in question [19].
One major set of examples of attributive classes involve roles. Thus ‘professor’ (defined as: a human
being who has the professor role) denotes an attributive class, and so also do ‘nurse’, ‘student’,
‘colonel’ and so forth.
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Attributive classes include also what we will call historical classes – classes whose members satisfy
some historical condition, for example: biological father, person identified as candidate for clinical
trial #2056-555, or person who has visited Pittsburgh.
For biological father, the correct form of definition is roughly as follows:
biological_father(a) =Def. a instantiates the universal human being
& a is male
& there some some zygote b
& there is some some child c
& there is some process of fertilization d
& b output_of c
& a agent_of c
& c = a.
Definitions
We distinguish between terms, which are lables for universals and attributive classes, and relational
expressions, which are labels for relations [16]. Definitions of terms are always of the form
an S =Def. a G which Cs
where ‘S’ (for: species) is the term to be defined, ‘G’ (for: genus) is the immediate parent term of ‘S’
in the relevant BFO-conformant ontology, and ‘D’ (for: differentia) specifies what it is about the G’s
which makes them S’s.
Attributive classes can be defined by using as genus any BFO-conformant universal below entity.
Relations of parthood
Primitive relations
a part_of b at t – where relata are continuants
a part_of b – where relata are occurrents
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The mereology used in each case is Simple Extensional Mereology as defined in [46].
Note that ‘part_of’ in BFO signifies always: ‘proper or improper part’. Thus every entity, from the
BFO point of view is, trivially, a part of itself.
Relations defined in terms of part-of
a has_part b = Def. b part_of a
a has_part b at t = Def. b part_of a at t
The above are instance-level relations; we will supply the associated type-level relations in a later
version of this document, along the lines set forth in [16].
2. Continuant
Elucidation: A continuant is an entity that persists, endures, or continues to exist through time while
maintaining its identity.
Axiom: if a is a continuant and b is part_of a then b is a continuant
(Continuants have no temporal parts.)
Theorem: if a is a continuant and a is part_of b then b is a continuant.
Axiom: if a is a continuant at some time, then there is some one-dimensional temperal region (some
temporal interval) during which a exists.
Note: Continuants may persist for very short periods of time (as for example in the case of a highly
unstable isotope).
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Relation of specific dependence
Elucidation: To say that a s-depends on b is to say that:
a exists
& a is of its nature such that, if for some t, a exists at t then b exists at t also
& a and b share no common parts.
Theorem: an entity does not s-depend on any of its parts.
However, the parts of an entity may s-depend on each other.
If a s-depends on b, then we can also say that a necessitates the existence of b; is tied of its nature to
b. If a s-depends, then it s-depends at every time at which it exists. If b is such that some a sdepends on it, then if b ceases to exist, so also does that something. The entities which s-depend
include dependent continuants, which s-depend either on each other or on the independent
continuants which are their bearers, and occurrents, which s-depend either on each other or on the
independent continuants which participate in them. [46, chapter 8; 20, 22]
Examples of one-sided s-dependence of a dependent continuant on an independent continuant:

a headache on a head

an instance of temperature on some organism

a smile on a human face

a process of cell death and a cell (where the ceasing to exist of the cell marks the end of the
process)
Examples of reciprocal s-dependence between dependent continuants:

roles of husband and wife [20]

three-sided reciprocal dependence of the hue, saturation and brightness of a color [45]

three-sided reciprocal dependence of the pitch, timbre and loudness of a tone [45]
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Examples of reciprocal s-dependence between occurrents:

a process of playing with the white pieces in a game of chess is reciprocally dependent on a
process of playing with the black pieces in the same game of chess

a process of buying and the associated equal and opposite process of selling

a process of increasing the volume of a body of gas at fixed temperature and the associated
process of decreasing the volume
Examples of one-sided s-dependence of one occurrent on another

a process of answering a question is dependent on a prior process of asking a question

a process of obeying a command is dependent on a prior process of issuing a command
2.1 Independent Continuant
A is an independent continuant = Def. a is a continuant which is such that there is no b such that a sdepends on b
Examples: an atom, a molecule, an organism, a heart, a chair, the bottom right portion of a human
torso, a leg; the interior of your mouth; a spatial region; an orchestra.
Note that the use of ‘of’ here (as in: ‘interior of your mouth’) does not indicate s-dependence. Sdependence holds only where the s-dependent entity or entities involved have what was traditionally
referred to as a ‘lesser degree of being’ than the associated independent continuant bearers (as a color
has a lesser degree of being than a colored thing).
Axiom: Every independent continuant is such that there are entities which inhere in it.
Examples: qualities, dispositions, processes.
Subtypes of independent continuant:
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material entity
object
fiat object part
object aggregate
immaterial entity
continuant fiat boundary
zero-dimensional continuant fiat boundary
one-dimensional continuant fiat boundary
two-dimensional continuant fiat boundary
site
spatial region
zero-dimensional region
one-dimensional region
two-dimensional region
three-dimensional region
2.1.1 Material entity
Elucidation: A material entity is an independent continuant that has some portion of matter as proper
or improper part. Thus every material entity is extended in 3 spatial dimensions.
Examples: human beings, undetached arms of human beings, aggregates of human beings.
Axiom: every entity which has a material entity as part is a material entity
Theorem: every entity of which a material entity is part is a also a material entity.
‘Matter’ here is intended in the sense of physics, as something which includes elementary
particles among its proper or improper parts: quarks and leptons at the most fundamental level of
granularity; protons, neutrons and electrons at a higher level of granularity; atoms and molecules at
still higher levels, forming the cells, organs, organisms and other material entities studied by
biologists.
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Material entities may have immaterial entities as parts – including the entities identified below as
sites; for example the interior (or ‘lumen’) of your small intestine is a part of you.
2.1.1.1 Object
BFO rests on the presupposition that the material universe is built to a large degree out of separate or
stable, spatially separated or separable units, combined or combinable into aggregates called groups,
populations, or collections. Many scientific laws govern the units in question, and the units play a
central role in almost all domains of natural science from particle physics to cosmology. The division
of reality into such stable natural units, and the fact that these units form aggregates such as families,
herds, populations, breeds, species, and so on, is at the heart of biological science. The division of
certain portions of reality into engineered units is the basis of modern industrial technology, which
rests on the distributed mass production of pre-engineered parts through division of labor and on their
reassembly into larger, compound units such as cars and laptops. The division of portions of reality
into units is the basis also of the phenomenon of counting. Clearly not all material entities form
separated or separable natural units in this way (see Figure 1 and [12]).
Figure 1: Mount Everest from space
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Examples of units of special importance for the purposes of natural science include: atom, molecule,
organelle, cell, organism, planet, star. These material entities are candidate examples of what called
‘objects’ in BFO. Each of the listed types of units is marked by the fact that it has very large numbers
of instances. Such units are often referred to as ‘grains’, and are associated with specific ‘levels of
granularity’ in what is seen as a layered structure of reality, with units at lower and more fine-grained
levels being combined as parts into grains at higher, coarse-grained levels. In what follows, however,
we shall formulate our proposals independently of any granularity considerations.
Elucidation of BFO:object
The following elucidation is provided not as part of a formal theory (of qualitative mereotopology [5,
5, 22, 36, 37, 39]), but rather as a set of conditions to be used when deciding whether entities of a
given type should be represented as objects in the BFO sense.
Preamble on the strategy
Material entities fall into different groups, for instance
-
of portions of solid matter, portions of liquid, portions of gas
-
collections of microparticles (which can survive through phase transitions from solid to liquid
to gas)
-
portions of energy (to be included in a future version of BFO).
In what follows we consider three candidate groups of examples of objects in the BFO sense,
namely:
1. organisms and cells
2. portions of solid matter such as rocks and lumps of iron
3. engineered artifacts such as watches and cars.
Material entities under all of these headings are all causally relatively isolated entities in Ingarden’s
sense [47, 13]. This means that they are both structured through a certain type of causal unity and
maximal relative to this type of causal unity.
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We first characterize causal unity in general, we then distinguish three types of causal unity
corresponding to the three candidate families of BFO:objects listed above. We then define what it is
for an entity to be maximal relative to one or other of these types, and formulate in these terms an
elucidation of ‘object’.
Elucidation: a is causally unified means: a is a material entity which is such that its material parts are
tied together in such a way that, in environments typical for entities of the type in question,

if a part in the interior of a is moved in space to a location on the exterior of a then either
a’s other parts will be moved in coordinated fashion or a will be damaged (be affected,
for example, by breakage or tearing)

causal changes in one part of a can have consequences for other parts of a without the
mediation of any entity that lies on the exterior of a
Material entities with no material subparts would satisfy these conditions trivially.
Candidate examples of types of causal unity for material entities of more complex sorts are as
follows (this is not intended to be an exhaustive list):
CU1: Causal unity via physical covering
Here the parts in the interior of the unified entity are combined together causally through a
common membrane or other physical covering. The latter points outwards toward and serves
as a protective function in relation to what lies on the exterior of the entity [13, 47].
Note that the physical covering may have holes (for example pores in your skin, shafts
penetrating the planet’s outer crust, sockets where conduits to other entities are connected
allowing transport of electric current or of liquids or gases). The physical cover is
nonetheless connected in the sense that, between every two points on its surface a continuous
path can be traced which does not leave this surface.
Some organs in the interior of complex organisms manifest a causal unity of this type.
Organs can survive detachment from their surroundings, for example in the case of
transplant, with their membranes intact. The FMA [44] accordingly defines ‘organ’ as
follows:
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An anatomical structure which has as its direct parts portions of two or more types of
tissue or two or more types of cardinal organ part which constitute a maximally
connected anatomical structure demarcated predominantly by a bona fide anatomical
surface. Examples: femur, biceps, liver, heart, skin, tracheobronchial tree, ovary.
CU2: Causal unity via internal physical forces
Here the parts of a material entity are combined together causally by sufficiently strong
physical forces (for example, by fundamental forces of strong and weak interaction, by
covalent or ionic bonds, by metallic bonding, or by van der Waals forces). In the case of
larger portions of matter the consistuent atoms are tightly bound to each other either in a
geometric lattice, either regularly (as in the case of portions of metal) or irregularly (as in
an amorphous solid such as a portion of glass).
CU3: Causal unity via engineered assembly of components
Here the parts of a material entity are combined together via mechanical assemblies
joined for example through screws or other fasteners. The assemblies often involve parts
which are reciprocally engineered to fit together, as in the case of dovetail joints, balls
and bearings, nuts and bolts. A causal unity of this sort can be interrupted for a time, as
when a watch is disassembled for repair, and then recreated in its original state. The parts
of an automobile, including the moving parts, constitute an object because of their
relative rigidity: while these parts may move with respect to each other, a given gear
cannot move e.g., 10 ft, while the other parts do not. Thus a raindrop on the car is not part
of it (nothing prevents it from being moved many feet away from the car) while the oil in
the crankcase, and various gears, are parts of the car.
We can now elucidate what it means for a material entity to be maximal relative to one or other of
these three types of causal unity.
Elucidation: a is maximal means that a is causally unified relative to some CUn and there is
no b which is also causally unified relative to CUn and which includes a as proper part.
Thus conjoined twins sharing vital organs are, prior to separation, not maximal relative to the CU1
type of causal unity.
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Elucidation: an object is a material entity which manifests causal unity of one or other of the
types listed above (or of some other type to be distinguished in the future) and is maximal
relative to the corresponding type of causal unity.
Each object is such that there are entities of which we can assert unproblematically that they lie in its
interior, and other entities of which we can assert unproblematically that they lie in its exterior. This
may not be so for entities lying at or near the boundary between the interior and exterior. (See Figure
2)
Figure 2: An example of cell adhesion
Some instances of any given BFO:object universal – for example cell or organism or laptop – are
separated by spatial gaps from other instances of this same object universal. The spatial gaps may be
filled by a lower-density medium, for example of air or water. (There are cells not adjacent to or
attached to other cells; there are spatially separated organisms, such as you and me.)
Objects may contain other objects as parts
They may do this for example

by containing atoms and molecules as parts
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
by containing object aggregates as parts, for instance the collection of blood cells in your
body is an object aggregate;

by containing objects which are bonded to other objects of the same type in such a way
that they cannot (for the relevant period of time) move separately, as in the case of the
cells in your epithelium or the atoms in a molecule.

in the case of organs (inside an organism) and some types of engineered constituents
(inside a physical artifact) parts may be separate (for example they may float in some
portion of liquid) or they may be connected together through conduits or tracts which
may themselves have covering membranes which themselves lie in the interior of the
object.
Some objects may also have immaterial parts (the lumen of your gut).
Axiom: Objects retain their objecthood for as long as they exist.
A human body continues to exist even after being buried in a pile of cement. A watch that has been
taken apart for repair ceases to exist for as long as it is disassembled.
2.1.1.2 Object aggregate
The term ‘aggregate’ will in a future version of BFO be defined in general terms, in such a way that,
for all continuant BFO categories X, the user of BFO will have at his disposal also the category
‘aggregate of X’ [51].
Elucidation: a is an object aggregate = Def. a is a material entity consisting exactly of a plurality of
objects as parts. More formally:
If a is an object aggregate, then if a exists at t, then there are objects o1, …, on at t such that:
for all x (x part of a at t iff x overlaps some oi at t)
Object aggregates may be defined through physical attachment (the aggregate of atoms in a lump of
granite), or through physical containment (the aggregate of molecules of carbon dioxide in a sealed
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container, the aggregate of blood cells in your body). Object aggregates may be defined by fiat – for
example in the case of the aggregate of members of an organization, or via attributive delimitations
such as ‘the patients in this hospital’, ‘the restaurants in Palo Alto’, ‘your collection of Meissen
ceramic plates’.
As is true for all material entities (for example: you), object aggregates may gain and lose object
parts while remaining numerically identical (one and the same individual) over time.
Candidate: Examples: a symphony orchestra, the aggregate of bearings in a crank shaft,
2.1.1.3 Fiat object part
a is a fiat object part = Def. a is a material entity that is a proper part of an object and that is,
relative to the object’s type of causal unity, not maximal.
Since fiat object parts are material entities, they are also extended in space in three dimensions (in
contrast to fiat continuant boundaries, introduced below).
Examples of fiat object parts: the upper and lower lobes of the left lung, the dorsal and ventral
surfaces of the body, the Western hemisphere of the Earth, the FMA:regional parts of an intact
human body.
Fiat object parts are contrasted with bona fide object parts, which are themselves objects (for
example a cell is a bona fide object part of an multi-cellular organism), and are marked by bona fide
boundaries, on in other words by physical discontinuities [8, 8]. Most examples of fiat object parts
are associated with theoretically drawn divisions, for example the division of the brain into regions,
the division of the planet into hemispheres, or with divisions drawn by cognitive subjects for
practical reasons the division of a cake (before slicing) into (what will become) slices. However, this
does not mean that fiat object parts are dependent for their existence on divisions or delineations
effected by cognitive subjects. If, for example, it is correct to conceive geological layers of the earth
as fiat object parts of the earth, then even though these layers were first delineated in recent times,
still they existed long before such delineation and truths about these layers (for example that the
oldest layers are also the lowest layers) did not become true because of any acts of delineation.
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Portions of matter are not extra entities
BFO (in contrast to DOLCE) is non-multiplicative; it does not distinguish between an object and its
constituting matter. The statue is not a second object; it is the portion of bronze during the period
when it plays the statue role.
If an entity is in one of the three categories – object, fiat object part, object aggregate – at any given
time in its existence, then it is so at all times. A leaf (plant organ) falls from a tree. A uterus is
explanted. An atom becomes bound up with other atoms in a molecule. A cell becomes bound with
another cell in an organism (both cells preserve their existence). A cell divides into two cells (the
first cell ceases to exist).
Note that object and fiat object part are by definition disjoint (in the sense that they are such as to
share no instances in common). However we do not assert that object and fiat object part are disjoint
from object aggregate. A pair of parts of your body – for example a pair of blood cells in your leg,
may simultaneously be both a fiat object part of your body and an object aggregate. A molecule may
simultaneously be both an object its own right and an object aggregate comprised of atoms. A watch
is simultaneously both an object and an aggregate of its component parts.
Treatment of material entity in BFO
Examples of problematic cases which might call forth such extensions include: a muscle on (and
attached to) a rock, a slime mold, a slice of cake, a pizza, a cloud, a galaxy, a railway train with
engine and multiple carriages, a clonal stand of quaking aspen, a bacterial community (‘biofilm’), a
polypeptide chain, a broken femur.
Where users of BFO need to annotate data pertaining to such problematic cases, then they may in
every case use BFO:material entity in formulating the corresponding annotations.
However it is clear that BFO will need to recognize other sub-universals of material entity, in
addition to object, object aggregate and fiat object part – for instance: aggregate of fiat object parts
[29]. Thus BFO:material entity should not be associated with any closure axiom and the existing
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treatment of the three identified sub-universals should not be associated with any claim to
exhaustivity.
We will provide a strategy for dealing with such sub-universals in a later version of this document.
Briefly, the proposal is that a central repository will be created where users of BFO can create BFOconformant extensions (embracing terms which meet the criterion that they are formal- rather than
domain-ontogical, and associating them with suitable definitions and examples). The terms in this
repository can then be adopted by others, according to need, and incorporated into BFO if adopted by
multiple communities of users.
2.1.2 Immaterial entity
The roots of BFO’s treatment of ‘immaterial entity’ lie in the application of theories of qualitative
spatial reasoning to the geospatial world for example as outlined in [49], in the treatment of holes by
Casati and Varzi [48], and the treatment of cavities in the FMA [43, 44, 34, 35].
Immaterial entities are divided into two subgroups:
1. sites and boundaries, which are tied to material entities, and which can thus change size,
shape and location as their material hosts move (for example: the boundary of Wales; your
nasal passage; the hull of a ship [38, 7, 10]);
2. spatial regions, which exist independently of material entities, and which thus do not change.
Immaterial entities under the former headings are in some cases parts of their material hosts.
Immaterial entities under both headings can be of zero, one, two or three dimensions.
We define:
a is an immaterial entity = Def. a is an independent continuant that has no material entities as parts.
2.1.2.1 Continuant fiat boundary
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a is a continuant fiat boundary = Def. a is an immaterial entity that is of zero-, one- or two
dimensions.
Axiom: A continuant fiat boundary is of n dimensions iff it is located at some n-dimensional spatial
region.
Every continuant fiat boundary is located at some spatial region at every time at which it exists (but
not necessarily at the same spatial region from one time to the next).
All material entities are of three dimensions. Intuitively, a continuant fiat boundary is a boundary of
some material entity (for example the plane separating the Northern and Southern hemispheres, the
North Pole), or it is a boundary of some immaterial entity (for example of some portion of airspace).
Three basic kinds of continuant fiat boundary can be distinguished (together with various
combination kinds):

fiat boundaries which closely coincide with the material surfaces of material entities or with
other physical discontinuities; when we program a telesurgical device for purposes of
targeting an incision through the surface of your skin, then we might represent this surface as
a two-dimensional plane (for the purposes of the device, the differences between this twodimensional fiat plane and the actual surface fall below the threshold of granularity [11])

fiat boundaries which delineate fiat parts within the interiors of material entities – for
example the fiat boundary between the northern and southern hemispheres of the Earth; the
North Pole; the fiat boundary which separates Utah from Colorado)

fiat boundaries which delineate holes or cavities, for example fiat boundaries of the type
referred to by the FMA under the heading ‘plane of anatomical orifice’.
An example of a combination fiat boundary would be the border of Denmark.
2.1.2.1.1 Zero-dimensional continuant fiat boundary
Elucidation: a zero-dimensional continuant fiat boundary is a fiat point whose location is defined in
relation to some material entity.
Examples: the North Pole; the quadripoint where the boundaries of Colorado, Utah, New Mexico,
and Arizona meet, the point of origin of some spatial coordinate system.
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2.1.2.1.2 One-dimensional continuant fiat boundary
Elucidation: a one-dimensional continuant fiat boundary is a continuous fiat line whose location is
defined in relation to some material entity.
To say that a one-dimensional continuant fiat boundary is continuous is to assert that it contains no
gaps.
Examples: The Equator, all geopolitical boundaries, all lines of latitude and longitude, the median
sulcus of your tongue.
2.1.2.1.3 Two-dimensional continuant fiat boundary
Elucidation: a two-dimensional continuant fiat boundary (surface) is a self-connected fiat surface
whose location is defined in relation to some material entity.
‘Self-connected’ here and in what follows is to be understood in the following (topological) sense;
thus to assert that an entity a is self-connected is to assert that given any two points in a, there is a
continuous line in a which connects these points.
From this it follows that a two-dimensional continuant fiat boundary (surface) may have holes, as for
example in the case of the surface of one side of a compact disk.
Examples: see Table 1.
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Table 1. Fragment of Foundational Model of Anatomy
Anatomical boundary entity
Anatomical surface
Bona fide anatomical surface
Anatomical plane
Anchored anatomical plane
Craniocervical plane
Cervicothoracic plane
Thoraco-abdominal plane
Occipital plane
Interspinous plane
Plane of anatomical orifice
Anatomical transverse plane
Plane of anatomical junction
Sagittal midplane of body
2.1.2.1.4 Site
a is a site = Def. a is a three-dimensional immaterial entity that is (partially or wholly) bounded by a
material entity or a three-dimensional immaterial part thereof.
Examples: a hole in the interior of a portion of cheese, a rabbit hole, the interior of this room, the
Grand Canyon, the Piazza San Marco, an air traffic control region defined in the airspace above an
airport, a kangaroo pouch, your left nostril, the hull of a ship, the lumen of your gut, the interior of
the trunk of your car, the interior of your refrigerator, the interior of your office, Manhattan Canyon)
Note: Sites may be bounded in part by fiat boundaries, as for instance the Mont Blanc Tunnel is
bounded by fiat boundaries at either end. Each immaterial entity coincides at any given time with
some spatial region, but, as in the case of material entities, which spatial region this is may vary with
time. As the ship moves through space, so its hull moves also. As you pinch and unpinch your nose,
your nostril dilates and expands.
The class A region of controlled airspace is a site, since it is a three-dimensional part of the site
formed by the sum of this region with the portion of the class E region that is bounded by the surface
of the Earth (see Figure 3).
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Figure 3: Airspace classes
Cavities within what Ontology for General Medical Science (OGMS) calls the ‘extended organism’
are sites; they are parts of the organism if they are part of its organisms anatomical Bauplan [43,
44]. Thus a cavity created by an incision with a knife is not a part of the organism.
1
2
3
4
Figure 4: Examples of types of site
1: the interior of an egg; 2: the interior of a snail’s shell; 3: the environment of a pasturing cow
2.1.2.3 Spatial region
In a later version of this document we will document the way in which every spatial and every
temporal region is dependent on a reference frame. (Spatiotemporal regions, in contrast, are
independent of reference frame.)
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We recommend that users of BFO:spatial region specify the coordinate frame which they are
employing. When dealing with spatial regions on the surface of the Earth, for example, this will be
the coordinate frame of latitude and longitude, potentially supplemented by the dimension of altitude
(height above sea level). Such coordinate frames can be associated with a Newtonian or a relativistic
frame of reference. The reference frame might be defined in relation to a moving object such as the
earth, in which case the corresponding spatial regions move with the movement of the earth.
However, they are at rest relative to their coordinate frame. Lines of latitude and longitude are twodimensional object boundaries which can move; however, they are by definition at rest relative to the
coordinate frame which they determine.
Elucidation: A spatial region is, intuitively, a zero-, one-, two- or three-dimensional part of the space
in which objects move and are located.
Spatial regions have no qualities except shape, size and relative location.
Object boundaries and sites are distinguished from the spatial region which they occupy at any given
time in the sense that (1) the former move when their material host moves, and they change shape or
size when their material host changes shape or size; (2) the latter must be specifiable in terms of
some system of coordinates, and they are by definition at rest relative to this coordinate frame.
2.1.2.3.1 Zero-dimensional spatial region
Elucidation: a point in space.
2.1.2.3.2 One-dimensional spatial region (aka spatial line)
Elucidation: a continuous line stretching from one point in space to another
Examples: an edge of a cube-shaped portion of space.
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2.1.2.3.3 Two-dimensional spatial region (aka spatial volume)
Def. a self-connected spatial region of two dimensions.
Examples: the surface of a sphere-shaped part of space, an infinitely thin plane in space.
When the dependence of spatial regions on reference frames is documented, then we will document
also the relations between spatial regions defined relative to the (reference frame that is determined
by the Earth), and the corresponding sites and continuant fiat boundaries.
2.1.2.3.4 Three-dimensional spatial region
Def. a self-connected spatial region of three dimensions.
Examples: a cube-shaped region of space, a sphere-shaped region of space,
Location relations
Located_at
Elucidation: a located_at r at t
This is a primitive relation between an independent continuant, a spatial region which it occupies,
and a time.
Axiom: every region is located_at itself at all times.
Axiom: if a located at r at t & a part_of a at t, then there is some r which is part_of r & such that
a located_at r at t.
Located_in
a located_in b at t = Def. a and b are material entities, and the region occupied by a is a (proper or
improper) part_of the region occupied by b.
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Examples: your heart located_in your body; this stem cell located_in this portion of bone marrow;
this portion of cocaine located_in this portion of blood.
Relation of containment
Elucidation: a contained_in b at t means: a is a material entity & b is a site & for all spatial regions
r1, r2, if a located_at r1 at t and b located_at r2 at t, then r1 part_of the of r2 & if b is moved a
sufficient distance in space then this will cause a to be moved also in virtue of its position in relation
to b. (To see why this additional condition is needed see [52].)
A site is something in which a material entity can be contained.
Note that there are other sub-universals of immaterial entity, in addition to site, continuant fiat
boundary and spatial region. For instance: aggregate of sites, aggregate of spatial regions. The
part of space occupied by a pair of non-adjacent cubes is not a spatial region but an aggregate of
spatial regions.
All parts of spatial regions are fiat parts, since no boundaries of spatial regions are physical
discontinuities.
2.2 Specifically dependent continuant
Relation of specific dependence
a s-depends on b at t = Def. a exists at t & a s-depends on b
a is a specifically dependent continuant =Def. a is a continuant which s-depends on some entity.
Sub-types of specifically dependent continuant recognized by BFO are:
quality
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relational quality
realizable entity
role
disposition
function
Examples: the mass of this tomato, the color of this tomato, the smell of this portion of mozzarella,
the disposition of this fish to decay, the role of being a doctor, the function of this heart: to pump
blood, the function of this key to open this lock and the reciprocally dependent disposition of this
lock: to be opened by this key, John’s love for Mary.
a inheres in b =Def. a is a dependent continuant & b is an independent continuant & a s-depends
on b
Inherence is a subrelation of specific dependence which holds between a dependent continuant and
an independent continuant.
a bearer_of b at t = Def. b s-depends on a at t or b g-depends_on a at t
‘Bearer’ is a shorthand term of convenience.
2.2.1 Quality
Elucidation: a quality is an specifically dependent continuant that, in contrast to roles and
dispositions, does not require any further process in order to be realized.
Solubility, in order to be realized or manifested, requires a process in which some solid piece of salt
or sugar participates. Their crystalline quality, in contrast, does not stand in need of any realization
process of this sort.
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Examples: the color of a tomato, the ambient temperature of a portion of air, the length of the
circumference of your waist, the shape of a nose, the mass of a piece of gold, the weight of a
chimpanzee.
Axiom: If an entity is a quality at any time that it exists, then it is a quality at every time that it exists.
For some qualities, e.g. surface color, s-dependence is not on the material bearer but rather on its
surface.
a quality_of b at t = Def. a is a quality & b is a material entity & a s-depends_on b at t
Qualities of spatial regions are restricted to qualities of size, shape and location.
2.2.1.1 Relational quality
There are relational qualities, for example: loves, taller_than, which have a plurality of independent
continuants as their bearers.
a is a relational quality =Def. for some independent continuants b, c and for some time t: a
quality_of b at t & a quality_of c at t & a and b have no parts in common
2.2.2 Realizable entity
a is a realizable entity = Def. a is a specifically dependent continuant that inheres in some material
entity and is of a type instances of which are realized in processes of a correlated type.
Examples: the role of being a doctor, the function of your reproductive organs, the disposition of
your blood to coagulate, the disposition of this piece of metal to conduct electricity.
Relation of realization
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Elucidation: if a realizes b at t, then there is some material entity c & a is a process in which c
participates at t & b is a disposition or role of which c is bearer.
Note that t here ranges over temporal intervals, rather than over instants of time (temporal
boundaries).
There are also reciprocal realizable dependent continuants (e.g. husband/wife; complementary
dispositions (for example of key and lock), as described in [28]).
Axiom: if a realizable entity is realized in a process p, then its bearer participates in p.
2.2.2.1 Role (Externally-Grounded Realizable entity)
Elucidation: a is a role means: a is a realizable entity which exists because its bearer is in some
special physical, social, or institutional set of circumstances in which the bearer does not have to be,
and is not such that, if it ceases to exist, then the physical make-up of the bearer is thereby changed.
‘Role’ is another name for what we might call an extrinsic or externally-grounded realizable entity.
An entity is a role not because of the way it itself is, but because of something that happens or
obtains externally. Examples include:

the role of an instance of a chemical compound to serve as analyte in an experiment

the role of a stone in marking a boundary

the role of a priest in baptizing an infant
Optionality of Roles
Because a role is not a consequence of the in-built physical make-up of its bearer, roles are optional
in the sense that the bearer of a role can lose this role without being thereby physically changed.
Most of the roles we here distinguish involve some form of social ascription or imputation.
Candidate non-social roles however include positional roles – for example a given protein plays the
role of peripheral membrane protein. The roles of a bacteria in giving rise to an infection, or of a
portion of water in helping to initiate the growth process of a seed, are also positional in this sense. In
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both cases we have many examples (of bacteria, of portions of water) only some of which are in the
position where they play, respectively, the infecting and the growth-supporting roles.
Having a role vs. playing a role
An entity can play a role, as when a passenger plays the role of a pilot on a commercial plane in an
emergency, or a pyramidal neuron plays the role occupied by a damaged stellar neuron in the brain;
but neither the person nor the pyramidal neuron have those roles.
Attributive role classes
The correct form for generating phase sortal expressions designating attribute classes and involving
reference to roles is as follows:

student(a, t) = Def. a has_role student role at t
Here ‘student(John, t)’ means: John is a member_of the attributive class student at t.
2.2.2.2 Disposition (Internally-Grounded Realizable entity)
Elucidation: a is a disposition means: a is a realizable entity which is such that (1) if it ceases to
exist, then its bearer is physically changed, and (2) its realization occurs when this bearer is in some
special physical circumstances, and (3) this realization occurs in virtue of the bearer’s physical makeup.
Examples:

an atom of element X has the disposition to decay to an atom of element Y

the cell wall is disposed to filter chemicals in endocitosis and exocitosis

certain people have a disposition to develop colon cancer

children are innately disposed to categorize objects in certain ways.
Unlike roles, dispositions are not optional. If an entity is a certain way, then it has a certain
disposition, and if its physical makeup is changed then it may lose that disposition. A disposition can
for this reason also be referred to as an internally-grounded realizable entity. That is, it is a realizable
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entity that is a reflection of the in-built or acquired physical make-up of the independent continuant
in which it inheres.
Dispositions exist along a strength continuum. Weaker forms of disposition are realized in only a
fraction of triggering cases. These forms occur in a significant number of entities of a similar type.
Each disposition type is associated with one or more characteristic realization process types –
instantiated by those processes in which it is realized. Dispositions may also be associated with
characteristic trigger process types – instantiated by processes (for example of being dropped on a
hard surface) in which they are realized.
Diseases are dispositions according to OGMS [27]. We are referring to disposition also when we
consider genetic and other risk factors for specific diseases. These are predispositions to disease – in
other words they are dispositions to acquire certain further dispositions. The realization of such a
predisposition consists in processes which change the physical makeup of its bearer in such a way
that parts of this bearer then serve as the physical basis for a disease. This physical basis is referred to
be OGMS as a disorder.
2.2.2.3 Function
A function is a disposition that exists in virtue of the bearer’s physical make-up and this physical
make-up is something the bearer possesses because it came into being, either through evolution (in
the case of natural biological entities) or through intentional design (in the case of artifacts), in order
to realize processes of a certain sort. Examples include:

the function of amylase in saliva to break down starch into sugar

the function of a hammer to drive in nails

the function of a heart pacemaker to regulate the beating of a heart through electricity
Functions are realized in processes called functionings. Each function has a bearer with a specific
type of physical make-up. This is something which, in the biological case, the bearer has naturally
evolved to have (as in a hypothalamus secreting hormones). In the artifact case, it is something which
the bearer has been constructed to have (as in an Erlenmeyer flask designed to hold liquid) or also (as
in the case of penicillin) selected for.
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It is not accidental or arbitrary that a given eye has the function to see or that a given screwdriver has
been designed and constructed with the function of fastening screws. Rather, these functions are
integral to these entities in virtue of the fact that the latter have evolved, or been constructed, to have
a corresponding physical make-up. Thus the heart’s function is to pump blood, and not merely to
make thumping produce sounds. The latter are by-products of the heart’s proper functioning. The
screwdriver’s function is in addition bound together with the disposition of the screw: the two are
reciprocally dependent on each other (a case of reciprocal generic dependence).
Like dispositions of other sorts, a function is an internally-grounded realizable entity: it is such that,
if it ceases to exist, then its bearer is physically changed. In some cases an entity may preserve its
function even while it is physically changed in ways which make it unable to function. For a lung or
attic fan to be non-functioning is an indication that the physical make-up of these things has changed
– in the case of the lung perhaps because of a cancerous lesion; in the case of the attic fan because of
a missing screw. But these entities then still have their functions; it is simply that they are unable to
exercise these functions until the physical defect is rectified, for example through clinical
intervention or mechanical repair. The entities would lose their function only if they were changed
drastically, for example by being permanently removed from the body in the case of the lung, or by
being irreparably crushed in the case of the attic fan.
We can distinguish two varieties of function, artifactual function and biological function. These are
not subtypes of BFO:function however, since the same function – for example: to pump – can exist
both in artifacts and in biological entities. Rather the relevant difference in type exists here on the
side of the respective bearers.
Defined relations:
a role_of b at t = Def. a is a role and a inheres_in b at t
a disposition_of b at t =Def. a is a disposition and a inheres_in b at t
a function_of b at t = Def. a is a function and a inheres_in b at t
2.3 Generically dependent continuant
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a g-depends on b at t1 = Def. a exists at t1 and b exists at t1 and for some type B it holds that (b
instantiates B at t1) and necessarily, for all t (if a exists at t then some instance_of B exists at t)
Axiom: if a g-depends on b at some time t, then a g-depends on something at all times at which it
exists.
a is a generically dependent continuant =Def. a is a continuant that generically depends on one or
more other entities.
Example: the pdf file on your laptop, the pdf file that is a copy thereof in my laptop; the sequence of
this protein molecule; the sequence that is a copy thereof in that protein molecule.
Where BFO’s specifically dependent continuants are subject to what we might call the axiom of nonmigration – they cannot migrate from one bearer to another – generically dependent continuants are
able to migrate, through a process of exact copying. The very same pdf file can be saved to multiple
storage devices, and thus it can exist in multiple copies.
We can think of generically dependent continuants, intuitively, as complex continuant patterns
(complex qualities) of the sort created by authors or designers, or (in the case of DNA sequences)
through the processes of evolution. Further examples of generically dependent continuants include:
the chessboard pattern, the Coca Cola logo, the pattern of a traffic sign. Each such pattern exists only
if it is concretized in some counterpart specifically dependent continuant – the pattern of black and
white squares on this wooden chessboard here before me; the pattern of red and white swirls on the
label of this Coca Cola bottle; the pattern of paint on this traffic signboard; your social security
number; your recipe for spaghetti carbonara.
Such patterns can be highly complex. The pattern of letters of the alphabet and associated
punctuation and spacing which is the novel Robinson Crusoe is concretized in the patterns of ink
marks in this and that particular copy of the novel. When you create a novel then in addition to
creating an s-dependent pattern of inkmarks on your manuscript, you create also a particular
instance of the generically dependent continuant type novel. When you print further copies in book
form, then you create multiple particular instances of the independent continuant type book.
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Relation of concretization
a concretizes b at t = Def. a is a specifically dependent continuant & b is a generically dependent
continuant & for some independent continuant c, a s-depends on c at t and b g-depends on c at t,
and if b migrates from bearer c to another bearer d than an exact copy of a will be created in d.
The data in your database are patterns instantiated as s-dependent quality instances in your hard
drive. The database itself is an aggregate of such patterns. When you create the database you create a
particular instance of the generically dependent continuant type database. Each entry in the database
is an instance of the generically dependent continuant type datum.
Data, databases, pdf files, novels, and other information artifacts are thus analogous to other created
artifacts such as paintings or sculptures. They differ from the latter, however, in that, once they have
been created, they can exist in many copies that are all of equal value. These many copies exist
because of a templating process. Only where such a templating process exists do we have the sorts of
patterns which are generically dependent continuants.
Generically dependent continuants can be concretized in multiple ways; you may concretize a poem
as a pattern of memory traces in your head. You may concretize a piece of software by installing it in
your computer. You may concretize a recipe which you find in a cookbook by turning it into a plan
which exists as a realizable dependent continuant in your head.
Axiom: if a g-depends on b at some time, then there is some c, a concretization of a, which sdepends on b.
Works of Music and Experimental Protocols
In the case of a work of music such as Beethoven’s 9th Symphony, there is a certain abstract pattern,
a generically dependent continuant, which we shall call #9. #9 is an instance of the type symphony,
which is itself a subtype of the type musical work. #9 is concretized in certain specifically dependent
continuant patterns of ink marks that we find in printed copies of its score, or in certain specifically
dependent continuant patterns of grooves in vinyl disks. The score is an instance of the generically
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dependent continuant type plan specification, specifying how to create a corresponding musical
performance. This plan specification is concretized in distributed fashion in the form of a network of
subplans distributed across the minds of the conductor and the members of the orchestra, together
forming a plan to create a musical performance of #9. This complex realizable dependent continuant
is then realized when conductor and orchestra work together to create a certain pattern of air
vibrations conforming to the score and audible to an audience.
Analogously, when a research team decides to perform an experiment following a published
protocol, the protocol itself is a generically dependent continuant instance of the type plan
specification. The leader of the research team concretizes this protocol in her mind to create that
specifically dependent realizable continuant which is her plan for carrying out this experiment. At the
same time she creates a series of sub-protocols, plan specifications for her various team members.
These plan specifications are concretized in the minds of the team members as plans for carrying out
corresponding subactivities within the experiment. The experiment itself is a realization of these
plans, having outputs such as publications, databases, and so forth, as described in the Ontology for
Biomedical Investigations (OBI).
3. Occurrent
The realm of occurrents is less pervasively marked by the presence of natural units than is the case in
the realm of independent continuants. Those natural which do exist in the realm of occurrents are
typically either parasitic on the existence of natural units on the continuant side (for example in the
cases of births and deaths, and of similar object-bound process boundaries), or they are fiat in nature.
Thus we can count lives; we can count football games; we can count chemical reactions performed in
experiments or in chemical manufacturing.
Even where natural units are identifiable, for example cycles in a cyclical process such as the beating
of a heart or an organism’s sleep/wake cycle, the processes in question form a sequence with no
discontinuities (temporal gaps) of the sort that we find for instance separating billiard balls or
zebrafish or planets by clear spatial gaps. Lives of organisms are process units, but they too unfold in
a continuous series from other pre-life processes such as fertilization and they unfold in turn in
continuous series of post-life processes such as post-mortem decay. Clear examples of boundaries of
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processes are almost always of the fiat sort (midnight, a time of death as declared in an operating
theater or on a death certificate).
Processes can be arbitrarily summed and divided. In particular, we can identify sub-processes which are
fiat segments occupying constituent temporal intervals of the temporal interval occupied by the process as
a whole – for example your heart-beating from 4pm to 5pm today; the 4th year of your life.
Elucidation: an occurrent is an entity that has temporal parts.
Examples: the life of an organism, a surgical, the spatiotemporal setting occupied by a process of
cellular meiosis, the most interesting part of Van Gogh’s life, the spatiotemporal region occupied by
the development of a cancer tumor.
Since temporal regions are temporal parts of themselves this means that 0-dimensional temporal
regions are also occurrents.
Subtypes of occurrent are:
process
process profile
process boundary
temporal region
zero-dimensional temporal region
one-dimensional temporal region
spatiotemporal region
Projection relations
spatiotemporal region projects_onto temporal region
spatiotemporal region projects_onto spatial region at t
Occupies relation
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Elucidation: a occupies r. This is a primitive relation between an occurrent and a temporal or
spatiotemporal region which it exactly occupies.
The occupies relation is the counterpart, on the occurrent side, of the relation located_at.
Trivially, every spatiotemporal or temporal region occupies itself.
Relation of temporal parthood
Elucidation: To say that a is a temporal_part_of b is to say that a part_of b & a and b are
occurrents & for some spatiotemporal or temporal region r, a occupies r & b occupies a region
including r as part.
Histories
The history of a material entity is the totality of processes taking place in the spatiotemporal region
occupied by the entity, including processes on the surface of the entity or within the cavities to which
it serves as host. (See the OGMS definition of ‘extended organism’.)
In the case of organisms histories are what we normally call ‘lives’ [15], and in the case of sentient
organisms lives will include also the experiences of the organism. If, for example, you experienced
the Second World War, then the Second World War is in this sense a part of (or better: is involved in
your history). The history of a material entity will include for instance the movements of neutrinos
within the interior of the entity as they pass through.
A revision is contemplated which would define the history of an entity as the sum of processes in
which that entity is the major participant.
The relation between a material entity and its history should be one-to-one.
Relation of boundary-dependence for occurrents
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a is boundary_dependent_on b = Def. a and b are occurrents & a temporal_part of b at t & a is
necessarily such that it cannot exist unless either (b exists or there exists some temporal_part of b
which includes a as temporal_part)
The missing ‘at t’ here signifies that this is a relation between occurrents
Process
p is a process = Def. a is an occurrent that has temporal proper parts and s-depends on one or
more material entities.
Examples: the life of an organism, the process of sleeping, the process of cell-division, a beating of
the heart, the process of meiosis, the course of a disease, the flight of a bird, the process of aging.
Just as there are relational qualities so also there are relational processes, which s-depend on multiple
material entities as their relata.
Examples: John thinking about Mary [3,4], John worrying about Mary, a moving body causing
another body to move.
Process boundary
p is a process boundary = Def. p is an occurrent entity which separates one process from another
immediately succeeding process & occupies a zero-dimensional temporal region.
Example: the boundary between the 2nd and 3rd year of your life.
a has_participant b =Def. a is an occurrent & b is a material entity & a s-depends on b.
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Process profiles
The problem of process qualities
In the case of a body moving with a constant speed, we can distinguish at least the following
elements:
(1) the body (object) that is moving
(2) the process of moving
(3) the temporal region occupied by this process
(4) the spatiotemporal region that is occupied by this process (trajectory of the motion)
(5) the determinate speed, a real-number magnitude referred to by means of
(6) an expression (information artifact, thus a BFO:generically dependent continuant) such as
‘3.12 m/s’.
Items (1)-(4) and (6) correspond directly to readily identifiable BFO categories. In regard to item (5),
it has been proposed that BFO recognize a new category of process quality, the counterpart on the
occurrent side of qualities of continuants. To see the problems with such an approach, consider the
following scenario, which is designed to illustrate the contrasting logico-ontological orders which
rule on the continuant (three-dimension) and occurrent (four-dimensional) side of BFO [14, 21, 30,
31, 32, 33].
Imagine, first, an independent continuant, John, an object, who, on a certain day, either does or does
not go on a one-month diet. In the former case his weight quality will decrease; in the latter case this
quality will remain constant. In either case John will remain at the end of the month the same
individual object as he was on the day in question.
In the case of a process, in contrast, no parallel scenario is imaginable. This is because there is no
way that the process which is John’s life could be imagined to vary under two different scenarios –
for example life with diet, life without diet – while remaining one and the same individual process.
itself would remain the same individual process. If something varied, then the process itself would be
a different process.
Why processes do not change
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Processes do not change, because processes are changes (they are changes, for example, with certain
rates, and happening at certain times and in certain orders). They are changes in those independent
continuants which are their participants.
The difference in logico-ontological order as between continuants and occurrents is captured in the
fact that instance-level parthood and other instance-level relations on the side of continuants, are
indexed by time; not however on the side of occurrents. As Galton and Mizoguchi point out [53],
persuasive arguments can be found in the literature (e.g., [54, 55, 56, 57]) that events cannot change:
The argument is essentially that the event as a whole occupies an interval of time; if in its
early stages the event has a certain property which it lacks in its later stages, then it is not the
event as a whole which either has the property or lacks it, but rather one part of the event has
the property and another part lacks it. Hence […] the event does not change.
For continuants, predications may need to be time-indexed in order to be true. For example, if a
instantiates larva at t, then it does not follow that a instantiates larva simpliciter. For occurrents, in
contrast, instantiation relations always hold simpliciter. This is because, while continuants can change
their type from one type to the next (e.g. a fetus becomes an embryo becomes an infant …), occurrents
can never change their type from one time to the next. Certainly an occurrent can for example involve
parts which are of different sorts in different times. A process of movement can, for example, have speed
v1at one time and then have a different speed v2at a later time. But there is then nothing in the realm of
occurrents which changes; rather, there is (simpliciter, un-time-indexedly) a process with two different
parts.
The solution to the problem
The treatment we propose rests on the insight that to predicate, for instance, ‘has speed 3.12 m/s’, to
a process of motion is to assert not that that the process has a special quality (which the same
process, in another conceivably have lacked) but rather that the process in question is of a certain
determinate type. The assertion that process p has speed v is thus analogous not to: rabbit r has
weight w, but rather to rabbit r instance_of the universal: rabbit.
But we can imagine, now, that process p is an instance not only of the universal 3.12 m/s motion
process, but also of the universal burning 9.2 calories per minute process, utilizing 30.12 litres of
oxygen per kilometer, and so on. (It may also instantiate universals such as: running process, be a
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cardiovascular exercise process, and many more.) The proposed solution thus threatens a
consequence which conflicts with the BFO rule of thumb that ontologies should as far as possible
avoid assertions of relations between universals which imply multiple inheritance [19].
How, then, is BFO to do justice to the need to annotate data in which speed or other putative qualities
are ascribed to bodily motions or other processes? The answer lies in the recognition that, when
measuring a process, it is in fact always only certain structural dimensions of the corresponding
whole processes to which the measurement datum directly relates. In the mentioned case these would
include for example structural parts pertaining to velocity of motion, energy consumed, oxygen
consumed. We shall in what follows call such structural dimensions process profiles.
Structural dimensions of qualities
The idea of process profiles as structural dimensions of processes has a counterpart in the world of
continuant qualities. Here, familiar, we can distinguish in every color quality instance three
dimensions of variation, corresponding to three inseparable color quality parts of hue, brightness and
saturation, tied together in a three-sided reciprocal dependence relation. An instance of colour-hue
cannot of its nature exist, except as bound up with some instance of brightness and saturation;
instances of brightness and saturation, similarly, cannot exist except as bound up with some specific
instance of hue [48, 49, 50], yielding a dependence structure of the sort depicted in Figure 5 [1, 2,
20]:
Figure 5: Three-sided reciprocal dependence
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where a, b, c, are instances of the three universals of hue (), brightness () and saturation (),
respectively.
Analogous dependence structures are found also in other sensory domains, for example in the three-sided
reciprocal dependence of the pitch, timbre and loudness which are the three structural dimensions of
a tone, and similar analyses can be used to describe the structures of cognitive and linguistic acts of a
range of different sorts [4, 58, 59].
To say that there are three dimensions of variation within each instance of color or tone is to assert means
that each such instance includes three structural parts – ‘structural’ in the sense that the parts in question
cannot exist except in the context of some whole of the given sort, including those other structural parts
upon which they are reciprocally dependent. Process profiles are parts of processes, but they are parts not
in the sense of ‘pieces’ (separable parts), but rather in the sense of inseparable structural parts. They are
entities which cannot exist except in the content of a surrounding whole of this given sort. They are
inseparable in the sense that, for example, for any given instance of your heart functioning as a pump, the
relevant motion and auditory profiles would necessarily be associated with some determinate blood
output profile.
There are, now, analogous structural dimensions of processes, which we call ‘process profiles’. The idea
is that for processes of each given sort, for example of bodily motion or of human metabolism, there is a
repertoire of such process profiles, and it is entities of this sort to which many of the assertions we make
about processes are directed. This idea has been advanced already under a different terminology in the
studies referenced in [50] on the variables encoded in physiology models used in the study of
physiological processes and represented in biophysical measurement data. Two particularly important
process profiles are those of respiration rate and pulse rate, as documented in the Vital Sign Ontology.
Bruno’s diary of weight gain and loss data represents a quantitative process profile of Bruno’s dieting
process.
Some examples of quantitative (measurable) process profile types, with subtypes provide for
illustrative purposes, include:

four-dimensional process shape profile (trajectory)

velocity profile
constant velocity profile
2 mph constant velocity profile
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3 mph constant velocity profile
increasing velocity profile

acceleration profile
constant velocity profile
0 ft/s2 acceleration profile
32ft/s2 acceleration profile
33 ft/s2 acceleration profile
increasing acceleration profile
The types and subtypes here are analogous to the types and subtypes of qualities recognized by BFOconformant ontologies on the continuant side, for example:
length
6 cm length
7 cm length
The user must however bear in mind, in both sets of cases, the subtypes in question, while they need
to be formulated using a specific unit of measure, are in fact unit-specification independent.
There are also non-quantitative process profiles, such as auditory process profiles (for example that
part of a given process of a heart’s beating which is audible (detectible by a given auditory
monitoring device)). More subtle examples of non-quantitative process profiles are provided by those
cases where symbologies exist for the recording of (the corresponding structural dimensions of)
processes of given sorts, for instance the profile of a chess game as captured in one or other of the
standard chess notations, is a process profile in the sense intended here, as also is the choreography
profile of a dance as captured in one or other of the standard choreographic notations.
Process profiles in human development are identified in the Anatomical Transformation Abstraction
(ATA) of the Foundational Model of Anatomy, which represents the ‘time-dependent morphological
transformations of the entities represented in the taxonomy during the human life cycle’ from
prenatal development to post-natal growth and aging’ [43].
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As we shall see, it is process profiles, not the circumcluding whole process, which instantiate the
corresponding (3.12 m/s, 9.2 calories/minute) universals represented in many different sorts of
process measurement data. Thus while quantitative values, and units of measure, are associated directly
with process profiles, but with the relevant whole processes only in a secondary sense.
Four-dimensional process shapes
Just as universals in general can be relatively determinable (as in the case of color) or determinate (as in
the case of orange of specific hue rgb(204, 90, 64), so also we can distinguish determinable and
determinate process profile universals.
As Johansson pointed out in his [42], processes involving motion or change of shape or size – any given
instance of your walking, for example – must have a certain determinable 4-dimensional process shape.
But which determinate shape is instantiated will of course vary from instance to instance.
Your specific process of walking is not itself an instance of the universal four-dimensional process shape.
Rather its process shape – this particular instance, the four-dimensional shape profile that belongs to it,
and to it alone, as structural part – is an instance of the universal four-dimensional process shape profile.
Rates and beat process profiles
In the draft Towards a Definition of Rate, we use the beat profile example to provide a preliminary
account of one important set of process predications, namely predications of rates to processes,
including processes whose rates are changing discontinuously or continuously. The account is
intended to apply to all processes with beat process profiles, including not only heart beat processes,
but also for example drumming processes, and simple cyclical processes (birthdays, …). Every
beating process is a beating process in virtue of its including some beat profile as a structural,
organizing process part. In addition to the regular beat profile (where a rate can be assigned in the
simplest possible), there is also an increasing beat profile, a decreasing beat profile, an accelerating
beat profile, as well as many other types of irregular beat profile, some of which, for example, for
example when they are detected in measurements of heart beat processes, may be clinically
significant.
How to deal with predications of processes
Each process profile is an instance-level part of some corresponding whole process. We can define:
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a process_profile_of b =Def. a and b are processes
& a proper part_of b
& there is some process c which is part of b and which is such that
a, b and c occupy the same temporal region
& a s-depends on c.
a is a process profile =Def. for some process b, a process_profile_of b
To assert, now, that a beating process has rate 4 bpm, is to assert that there is some beat profile which is a
part of this process and which occupies the same temporal interval as this process and which
instantiates the determinate universal: 4bpm beat profile.
More generally:
‘p has F of value n as measured in unit u’ abbreviates:
there is some process profile po such that
po part_of p
& po occupies the same temporal interval as p
& po instance_of the determinable process profile type: F
& po instance_of the determinate process profile type: F with magnitude n as
measured in unit u.
States as Static Process Profiles
For many process profile types we can distinguish an associated static (or ‘null’) process profile type.
Thus for example a null beat profile is a beat profile in which there are zero beats per interval of
time; a null velocity profile is one in which velocity is zero; a null acceleration profile is one in
which acceleration is zero, and so on.
Processes with null process profiles are often called ‘states’ (state of rest, state of uniform motion,
…). ‘States’ are special sorts of processes (they are processes in which, along the relevant dimension,
nothing happens). Such states can be highly complex: consider the case in which two equal and
opposite dispositions of attraction and repulsion can counterbalance each other – the dispositions are
realized but there is no movement.
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For every continuant entity there is what we might call its existence profile, which is a process
profile which is a part of the history of the entity in question, and which has only one state, called
‘exists’.
Summing Process Profiles
The auditory process profile of the morse code signal for ‘SOS’ has the following structure:
...
– – – ...
This is built by summation out of successive basic auditory process profiles of three types, called
dots, dashes, and spaces (null auditory process profiles), respectively. Between each dot or dash
within a single letter there is a single space; between successive letters there are three spaces.
Clearly, the process profiles here can be combined in arbitrary strings. If one morse code string is
followed by another, then the auditory process profile of their sum is equal to the sum of their
respective auditory process profiles. The heart beating process is the sum of two mutually dependent
systolic and diastolic processes (along the lines depicted in Figure 6).
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Figure 6: Cardiac Cycle, Left Ventricle
There seems to be a general law for process profiles:
Given any processes p1, … pn which share a specific type T of process profile and which do
not overlap in time:
T-process-profile(p1 +…+ pn) = T-process-profile(p1) + … + T-process-profile(pn)
Note that, in the morse code and similar cases, summation of process profiles has an exact
counterpart in the linear composition of generically dependent information artifacts (alphanumeric
strings) on the continuant side.
Comparing Qualities and Comparing Process Profiles
A further issue that we can now address is that of data involving comparison of process profiles (for
example to the effect that one process is quicker, or more intense, or of higher frequency, than that
process. He, too, it is useful to begin with the counterpart case on the side of qualities.
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For a given determinable quality universal Q, we employ ‘DSU(Q)’ as an abbreviation for ‘the
determinate sub-universals of Q’. For example if Q is the quality universal length, then DSU(Q)
comprises such determinate quality universals as: 1 cm-length, 1.5 cm-length, 2 cm-length, and so
on. Again, quality universals are referred to here in a way that involves specification of a unit of
measure; however, the universals themselves are clearly independent of such specification.
Since the qualities in DSU(Q) can here be ordered linearly in reflection of the real number measures
used to described them, we can define ‘shorter-in-length than’ in terms of ‘less than’ for real
numbers. In this sense the structure of DSU(Q) explains how length qualities relate to each other.
And now the parallel case on the side of occurrent side can be described as follows. For a given
determinable process profile universal P, we employ ‘DSU(P)’ as an abbreviation for ‘the
determinate sub-universals of P’. For example if P is the process profile universal regular beat, then
DSU(P) comprises such determinate process profile universals as: 1 beat per minute (bpm), 1.5 bpm,
2 bpm, and so on. Again, process profile universals are referred to here in a way that involves
specification of a unit of measure; however, the universals themselves are clearly independent of
such specification.
And again: DSU(P) is ordered linearly, so that there is an isomorphism from DSU(P) to the real
numbers, and we can define ‘beats faster than’ accordingly in terms of ‘greater than’ for real
numbers, and there is a sense in which the structure of DSU(P) explains how beat processes relate to
each other in terms of faster and shorter.
Spatiotemporal region
Def. An occurrent entity that can be occupied_by a processes .
Each spatiotemporal region projects_onto some temporal region.
Each spatiotemporal region projects_onto some spatial region at t.
The projection relations must be defined in every case in terms of the reference frame employed.
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Examples: the spatiotemporal region occupied by a human life, the spatiotemporal region occupied
by the development of a cancer tumor, the spatiotemporal setting occupied by a process of cellular
meiosis.
Temporal region
Elucidation. An occurrent entity that is part of time (defined always in relation to some reference
frame).
A temporal region is an occurrent entity upon which a process can be projected.
Zero-dimensional temporal region
A temporal boundary of a temporal region.
Examples: right now, the moment at which a finger is detached in an industrial accident, the moment
at which a child is born, the moment of death.
Synonym: temporal instant.
One-dimensional temporal region
Example: the temporal region during which a process occurs.
continuant
independent continuant
material entity
object
fiat object part
object aggregate
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immaterial entity
continuant fiat boundary
zero-dimensional continuant fiat boundary
one-dimensional continuant fiat boundary
two-dimensional continuant fiat boundary
site
spatial region
zero-dimensional region
one-dimensional region
two-dimensional region
three-dimensional region
specifically dependent continuant
quality
relational quality
realizable entity
role
disposition
function
generically dependent continuant
occurrent
process
process profile
process boundary
temporal region
zero-dimensional temporal region
one-dimensional temporal region
spatiotemporal region
BFO Relations
To be dealt with in the next version of this document.
References
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1. Barry Smith, “Logic, Form and Matter”, Proceedings of the Aristotelian Society,
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